Mass-transfer coefficients calculation

Table 3.1 shows the kinetic parameters for cell growth, rate models with or without inhibition and mass transfer coefficient calculation at various acetate concentrations in the culture media. The Monod constant value, KM, in the liquid phase depends on some parameters such as temperature, initial concentration of the carbon source, presence of trace metals, vitamin B solution, light intensity and agitation speeds. The initial acetate concentrations in the liquid phase reflected the value of the Monod constants, Kp and Kp. The average value for maximum specific growth rate (/xm) was 0.01 h. The value... 

Using Equation (13), the external mass transfer coefficient at 723 K was calculated to be 60 cm/s. Since the reactor operating conditions at th s temperature (723 K, slightly above atmospheric pressure, 247 cm /s) were very similar to those of our transient chemisorption experiments, the external mass transfer coefficient calculated above was used for the simulations. 

Table I liquid side mass transfer coefficient calculated with the penetration theory...

The model I is very simple, and it is not very sensitive to the physical properties of the bed, but the values of the overall mass transfer coefficients optimised are strongly dependent from the equilibrium relation assumed and it only is able to describe the initial part of the extraction. Ke was determined by mass balance assuming a uniform distribution in solid bed. Ke values of 0.5, 0.2, and 0.6 were obtained for 7, 10 and 15 MPa. Assuming a = 3000 nAn", the mass transfer coefficients calculated with model I are of some orders of magnitude lower than those for external mass transfer coefficients. This type of models have being applied with success to the extraction of edible oils from seeds were the solute is in a... 

Arve and Liapis [34] suggest estimating the parameters characterizing the intraparticle diffusion and the adsorption-desorption step mechanisms of affinity chromatography from the experimental data obtained in a batch system. The numerical simulations of the chromatographic process will use the values of the parameters of the adsorption isotherm and those of the effective pore diffusion as determined from stirred tank experiments together with the film mass transfer coefficients calculated from chemical engineering expressions found in the literature. 

Mass-transfer coefficients calculated from average absorption efficiency. More than 10 measurements were averaged for each coefficient value. 

In their original development of the linearized theory Toor (1964) and Stewart and Prober (1964) proposed that correlations of the type given by Eqs. 8.8.5 and 8.8.7 could be generalized by replacing the Fick diffusivity D by the charactersitic diffusion coefficients of the multicomponent system that is, by the eigenvalues of the Fick matrix [ >]. The mass transfer coefficient calculated from such a substitution would be a characteristic mass transfer coefficient an eigenvalue of [/c]. For example, the Gilliland-Sherwood correlation (Eq. 8.8.5) would be modified as follows ... 

This set of equations is compatible with the mass transfer coefficients calculated in Example 16.4 and is listed in rows 3 and 8 of Table 16.4. 

Mass transfer coefficient calculated using heat/mass analogy... 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

When it is known that Hqg varies appreciably within the tower, this term must be placed inside the integr in Eqs. (5-277) and (5-278) for accurate calculations of hf. For example, the packed-tower design equation in terms of the overall gas-phase mass-transfer coefficient for absorption would be expressed as follows ... 

Simplified Mass-Transfer Theories In certain simple situations, tne mass-transfer coefficients can be calculated from first principles. The film, penetration, and surface-renewal theories are attempts to extend tnese theoretical calculations to more complex sit-... 

Example 9 Calculation of Mass-Transfer Coefficient Group. 12-15... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Principles of Rigorous Absorber Design Danckwerts and Alper [Trans. Tn.st. Chem. Eng., 53, 34 (1975)] have shown that when adequate data are available for the Idnetic-reaciion-rate coefficients, the mass-transfer coefficients fcc and /c , the effective interfacial area per unit volume a, the physical solubility or Henry s-law constants, and the effective diffusivities of the various reactants, then the design of a packed tower can be calculated from first principles with considerable precision. 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

The bubbles shapes in gas purging vary from small spherical bubbles, of radius less than one centimen e, to larger spherical-cap bubbles. The mass transfer coefficient to these larger bubbles may be calculated according to the equation... 

To apply the mass transfer equation for design, the interfacial area, a, and mass transfer coefficient kL must be calculated. The interfacial area is dependent upon the bubble size and gas hold-up in the mixing vessel as given by ... 

Dl = diffusivity of transferring solute in liquid, m /sec If the diffusivity, Dl, needed for use in the above equations is not known, it can be estimated from data or methods given in the Perry s Chemical Engineers, Handbook (Section 14 in 4th Edition or Section 3 in 5th Edition). Note that the calculation of the mass transfer coefficients for a given regime involves only physical properties and is independent of agitation conditions. 

The performance equation of a mixer relates mixer size or mixing time to the input and output of the mixing device. The rate of transfer, r, incorporates the mass transfer coefficient, kL, and interfacial area, a, as calculated above. This rate can be used in conjunction with a material balance to relate concentrations of interest to time or size variables. 

Given this evaporation rate, the overall mass transfer coefficient may then be calculated from Equation 4-391,... 

The mass transfer coefficient is calculated for a given diffusivity coefficient and reaction rate constant at the equilibrium concentration of oxygen. When oxygen is continuously transported and removed from the liquid phase we may write ... 

The plot of the rate of disappearance of CO per volume of liquid in the serum bottles versus partial pressure of CO in the gas phase based on (3.14.4.14) could give the constant slope value of KLa/H. Henry s constant is independent of the acetate concentration but it is only dependent on temperature. The overall volumetric mass transfer coefficient can be calculated based on the above assumption. The data for various acetate concentrations and different parameters were plotted to calculate the mass transfer coefficient. 

Substituting Vs and VL into the above equation determines the volumetric mass transfer coefficient. Volumetric mass transfer coefficient is calculated as ... 

Specific sugar consumption rate = 1.0kg-kg 1 cell h 1 The mass transfer coefficient is calculated by the following correlation... 

Calculate mass transfer coefficient in a 60 m3 fermenter with a gas and liquid interfacial area of a = 0.3 m2-m 3, given pbroth = 1200kg m-3. The small reactor has working volume of 0.18m3, 1 vvm aeration rate. Oxygen transfer rate (OTR) is 0.25kmol in 3 h 3. There are two sets of impellers, and flat-blade turbine types of impeller were used, HL= 1.2/),. Find the exact specifications of a large fermenter. 

In evaluating their results they assumed the film theory, and, because the oxygen is sparingly soluble and the chemical reaction rate high, they also assumed that the liquid film is the controlling resistance. The results were calculated as a volumetric mass-transfer coefficient based, however, on the gas film. They found that the volumetric mass-transfer coefficient increased with power input and superficial gas velocity. Their results can be expressed as follows ... 

Yoshida and Miura (Y3) reported empirical correlations for average bubble diameter, interfacial area, gas holdup, and mass-transfer coefficients. The bubble diameter was calculated as... 

It is necessary to calculate mass transfer coefficients between a fluid and the surface of a particle in a number of important cases, including ... 

In the design of commercial units, nomographs 18,19 are available which give a performance characteristic (KaV/L ), where AT is a mass transfer coefficient (kg water/m2s) and V is the active cooling volume (m3/m2 plan area), as a function of 9, 9W and (V G ). For a given duty (KaV/L ) is calculated from ... 

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